I Nord~c 1 OECD
GBOWTH AND TECHNOLOGY:
2. MAIN FEATURES OF THE TAIWANEXE MODEL
The model i s essentially a n annual aggregative model of t h e Keynesian type, whose sample period i s 1960-81. The equations and variables of t h e estimated model are listed in t h e Appendix. In general, t h e method of estimation i s ordinary l e a s t squares.
9
i s t h e measure of goodness of f i t adjusted f o r d e g r e e s of f r e e - dom; and D.W. i s t h e Durbin-Watson statistic. The figure in p a r e n t h e s e s below e a c h regression coefficient indicates i t s t-value. Some of t h e equations are estimated by t h e Cochrane-Orcutt i t e r a t i v e method, where p i s t h e s e r i a l correla- tion coefficient of t h e f i r s t order in error terms.The f i r s t important c h a r a c t e r i s t i c of t h e model i s t h e disaggregation of e x p o r t s and imports, which enables us t o deal with t h e t r a d e relationship between Taiwan and Japan. Imports are then disaggregated into imports from Japan and those from c o u n t r i e s o t h e r than Japan. Imports from Japan are f u r t h e r disaggre- gated into six items: (1) food and agricultural products, (2) chemicals, (3) textiles, (4) metals, (5) machinery, and (6) others. These imports are mainly explained in terms of t h e GDP of Taiwan, r e l a t i v e p r i c e s , and t h e level of capacity output of Taiwan (see eqs. (2.1) t o (2.6)) The level of capacity output, r e p r e s e n t i n g t h e e f f e c t of import substitution, is calculated from t h e estimated production function, as explained below.
Imports from countries o t h e r than Japan are disaggregated into (1) fuels and (2) nonfuels. These are also explained in terms of t h e GDP of Taiwan and r e l a t i v e p r i c e s (eqs. (2.11) and (2.12))- T h e r e i s a slight statistical discrepancy between t h e sum of disaggregated imports from Japan and t h e total import from Japan, MGJPMO, since t h e former i s based on MITI t r a d e s t a t i s t i c s from Japan and t h e latter on t r a d e s t a t i s t i c s from Taiwan. The two figures are i n t e r c o r r e l a t e d through a statistical equation (eq. (2.19)). The sum of commodity imports from Japan and nonfuel commodity imports from countries o t h e r than Japan i s t h e total nonfuel commodity import, MO PMO, (eq. (2.18)), a n d the total commodity import and s e r v i c e imports add up to t h e imports of goods and s e r v i c e s derived from t h e national income account, M , (eq. (2.14)).
Commodity exports are also disaggregated into exports to Japan and those t o countries o t h e r than Japan. Exports to Japan are f u r t h e r disaggregated into (1) food and agricultural products, (2) chemicals, (3) machinery, and (4) others. The main explanatory variables f o r such exports a r e t h e GNP of Japan, relative prices, and the level of t h e capacity output of Taiwan (eqs. (2.7) to (2.10)). The second of these variables is introduced to take into account the fact that t h e capa- city level may impose limits on the maximum amount of Taiwanese exports. A g r e a t e r p a r t of item (4) is textiles. Therefore, in the estimation of eq. (2.10) w e used an estimate of 0.64 f o r t h e long-run elasticity of exports of this item with respect to the GNP of Japan; this estimate is the result of the calculation 1.26 x 0.79 x 0.64, where 1.26 and 0.79 a r e , respectively, estimates of t h e elasticity of consumer demand f o r textiles with respect to total consumption and the elasticity of total consumption with respect to personal disposable income, both of which were obtained from a cross-section study, and 0.64 is the r a t i o of personal dispos- able income to GNP.
Exports to countries other than Japan are explained in terms of the world trade index, relative prices, and the level of capacity output of Taiwan (eq.
(2.13)). In the same way as f o r imports, eqs. (2.21) to (2.24) are identities and sta- tfstical discrepancy equations, by which individual export items add up to exports of goods and services derived from t h e national income account, X.
The second significant feature of t h e model is the system of price equations that relates the growth of exports and imports to t h e cost s t r u c t u r e of domestic Taiwanese products. Corresponding to t h e disaggregation of imports, industry as a whole is disaggregated into eight industries: (1) primary, (2) food, (3) textiles, (4) chemicals, (5) petrochemicals, (6) metals, (7) machinery, and (8) construction, util- ities, and services.
Using the framework of input-output analysis, w e may write t h e price-cost relationship of industry i as:
Here P i , W, and PI a r e , respectively, the price f o r industry i , the wage index, and t h e deflator f o r investment goods; A ( j ,i ), LC(% ), D ( i ), T ( i ) , and S ( i ) are material input coefficients, labor input coefficients, t h e depreciation ratio, the indirect tax
ratio, and t h e surplus r a t i o , respectively. The coefficients, which r e p r e s e n t t h e technical and institutional structure of each industry, are adopted f r o m t h e Taiwanese input-output t a b l e f o r 1976. By solving e a c h equation with r e s p e c t t o P i , w e may e x p r e s s t h e p r i c e of domestic product i as a function of t h e p r i c e s of o t h e r products and t h e wage:
where PiD i s t h e p r i c e of t h e domestic product. This equation implies t h a t t h e cost of product t consists of two parts: t h e nonwage p a r t (the f i r s t term on t h e right-hand side) and t h e wage p a r t (the second term). Let us denote t h e former by Pi 10, as shown in eq. (4.2). The elasticity of PiD with r e s p e c t t o Pi I0 in t h e base y e a r , when Pi
=
1.0, i s calculated asIn eqs. (4.3). (4.6), (4.7), (4.9). and (4.10) the coefficient of h P i I 0 i s s e t at t h e value given by formula (A.3) from t h e 1976 input-output table. On t h e o t h e r hand, taking into account t h e distinct declining t r e n d in LC(i), w e introduced t h e r e c i p r o c a l of t h e l a b o r productivity of industry as a whole into eqs. (4.3) to (4.10) as a variable representing t h e secular movement of the l a b o r input coefficient of
industry t . In this p r o c e d u r e we assume t h a t t h e r e exists a s t a b l e relationship between t h e growth rates of labor productivity in industry as a whole and in t h e individual industry i
.
The p r i c e as a c o s t item, o r t h e p u r c h a s e r s ' p r i c e , P i , will b e defined as a weighted a v e r a g e of t h e p r i c e s of t h e domestic product, P i D , and t h e p r i c e of imported goods, Pi M (eq. (4.1)). The latter is also defined as a weighted a v e r a g e of t h e import p r i c e from Japan, PMJi.R4ZE, and the impol-t p r i c e s from countries o t h e r than Japan, PAE and PMO (eqs. (4.27) to (4.34)).
The deflators of individual components of final demands, PC, etc., a r e related t o a variable defined as a weighted a v e r a g e of t h e individual industry prices, PCIO, etc. (eqs. (4.12) to (4.16)), where t h e weight i s calculated from t h e relative s h a r e of each industry's output in t h e relevant final demand (eq. (4.11)).
Export prices,
mi,
are explained in terms of t h e p r i c e of t h e industry corresponding t o each e x p o r t item (eqs. (4.17) to (4.20)). Import p r i c e s from Japan, P W i , are determined by t h e wholesale p r i c e index of industry as a whole in US dollar terms, PWHIJ-RATJ (eqs. (4.21) t o (4.26)); w e assume t h a t t h e r e exists a 'stable relationship between t h e t r e n d of t h e p r i c e f o r industry as a whole and those f o r individual industries. Under t h e same assumption, t h e wholesale p r i c e index f o r each individual industry is r e l a t e d to t h a t of industry as a whole (eqs.(J.1) t o (5.4)).
The third important f e a t u r e of t h e m o d e l is t h a t t h e supply side of t h e econ- omy is r e p r e s e n t e d by a production function of t h e CES type:
where a n output variable, G P M , is t h e total supply, i.e., GDP plus imports, and L , M F , M E , and MO a r e l a b o r input, capital stock, fuel imports, and o t h e r imports, respectively; di and 9 are parameters and t h e elasticity of substitution is 1/ ( 1
+
3). Technical p r o g r e s s of a laboraugmenting type is allowed f o r by a trend variable T. W e assume t h a t t h e level of technical knowledge is expressed by an index, e x p (At), where t is a time trend, and t h a t t h e level of embodied tech- nique in existing plant and equipment at time t , Tt, is r e p r e s e n t e d by a weighted average of exp (At) o v e r t h e preceding t e n y e a r s , where t h e weight is new invest- ment o v e r t h e same period (eq. (5.1)). Cost minimization under eq. (A.4) gives us a set of f o u r log-linear m a r g i n d productivity relations, each of which h a s a dif- f e r e n t constant term but a common elasticity of substitution, u. Pooling t h e pro- ductivity and p r i c e d a t a f o r f o u r inputs yields t h e estimated r e s u l t s in eq. (5.1), where t h e whole sample period i s divided into two periods: before and a f t e r t h e oil crisis. Eq. (5.1) h a s t h e smallest residual sum of s q u a r e s among t h e equations obtained by assigning to A various values within a plausible range. Estimated r e s u l t s show t h a t t h e a v e r a g e annual rate of p r o g r e s s in available technical knowledge, A, is 7 and 6 p e r c e n t p e r y e a r f o r t h e y e a r s 1962-69 and 1974-81, respectively, while t h e elasticity of substitution, about 0.4, is almost t h e same f o rboth periods.
Capacity output i s defined as t h e value of GDPM obtained by substituting l a b o r f o r c e W;E f o r L in t h e estimated version of eq. (A.4) (namely, eq. (5.2)).
Since GDPM is t h e output of t h e whole economy, l a b o r input must include self- employed and family workers, NU, as well as employees, NW. In view of t h e l a r g e differential between t h e productivities of these types of input, however, l a b o r input is defined h e r e as t h e sum of IYW and a discounted NU, where t h e discount r a t e is t h e income differential, Dn (eqs. (6.4) to (6.9)). The desired level of L , 1.e. L I , is calculated from t h e marginal productivity f o m u l a f o r l a b o r (eqs. (5.1) and (6.1)). The actual level of L is regressed on this desired level and a lagged value of L (eq. (6.2)). Finally, a version of t h e Phillips c u r v e is estimated to d e t e r - mine t h e wage level of employees (eq. (6.10)).